A cockroach of mass m lies on the rim of a uniformdisk of mass 4 m that can rota

Question

A cockroach of mass m lies on the rim of a uniformdisk of mass 4m that can rotate freely about its centerlike a merry-go-round. Initially the cockroach and disk rotatetogether with an angular velocity of 0.Then the cockroach walks halfway to the center of thedisk.
What then is the angular velocity of the cockroach-disksystem? State your answer in terms of the given variables. A cockroach of mass m lies on the rim of a uniformdisk of mass 4m that can rotate freely about its centerlike a merry-go-round. Initially the cockroach and disk rotatetogether with an angular velocity of 0.Then the cockroach walks halfway to the center of thedisk.
What then is the angular velocity of the cockroach-disksystem? State your answer in terms of the given variables.

Explanation / Answer

initial moment of inertia: .        disk:   (1/2)(4m)R2           roach:   mR2 . final moment of inertia: .        disk:   (1/2)(4m)R2           roach:   m(R/2)2 . So...      initial moment ofinertia =   2mR2 + mR2 = 3mR2 .              final moment of inertia = 2mR2 + (1/4) mR2 =   2.25 mR2 . By conservation of angular momentum... .          initial angmom = final ang mom .         initial moment ofinertia * initial ang speed = final moment of inertia *final ang speed .          3mR2 * o   = 2.25mR2 * .    finalspeed = =    1.333o   or     (4/3)o . By conservation of angular momentum... .          initial angmom = final ang mom .         initial moment ofinertia * initial ang speed = final moment of inertia *final ang speed .          3mR2 * o   = 2.25mR2 * .    finalspeed = =    1.333o   or     (4/3)o

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